Solow Model

Basic Production function showing diminishing returns and equilibrium output where new investment only just offsets depreciation.

How fast does it converge? I took the basic framework and turned it into an excel spreadsheet. For this set:

Yt-1 = At-1Kαt-1L1-αt-1.

It-1=sYt-1.

Kt=Kt-1-δKt-1+It-1

With constant L and A you can then calculate the next row, and replicate to do the next 100…

The bottom line is that it converges quickly. Investment-led growth doesn’t last for long.

If you let the LF grow (here at a constant percentage rate) the equilibrium level of output per person is a bit lower, but not by much. Otherwise the dynamics are identical.

Put in productivity growth and everything changes. This growth has the LF expanding at 1% pa, as above, which pulls down growth. Add in even 0.5% pa productivity growth and suddenly you keep going past the 0.75 level at which output stabilized in our LF growth case. As per the rule of 70, at 0.5% growth it takes 140 years to double, but that’s close to 25% over a 40-year working life. Not good, but enough to be noticeable.